You think we could make our pet have their own taste?
Like it dislike apples, but love bananas.
You could know which one it loves and hates by giving it every item(it's not necessary actually, just feed, play him normally until you know it).
When/How would we know when it dislikes/likes this item?
I think it might be simple. Whenever your pet is hungry, and you fed an apple.
But he rejects the apple (then a page said "{Pet's name} didn't eat the apple").
For the 'like' part, for example you fed it a banana. Then a page said "{Pet's name} wants more bananas! It enjoys blablablabla"
Maybe you got some little RC if you found it's favorite food and when you found it's 'don't like' food, it's happiness minus a bit.
{the item doesn't have to be food, it could be toys, accercories, petpals,etc as well}